Are you using the Mendix feedback widget from the Appstore?
It seems to be a problem with the widget. I'll look into it but I suggest you file a support ticket either way.
What exactly do you want to achieve? If you want to have that button for userrole x and not for userrole y, this can easily be achieved.
In that case, make for each role an (alternative) homepage (2 separate pages), where the page for userrole x HAS the feedback widget and the one for y does NOT have it.
When a user has "seen" a page where that widget is placed, it will stay active until a browser-close.
Does this answer your question?